### Statistics Question

May. 17th, 2016 03:38 pm*C*of objects. I have a sample of objects of the class. And each object

*O*has its own sample with a number of trials

*N*.

_{O}*N*has a range of 1 to several hundred.

_{O}Each object

*O*has a parameter

*P*.

_{O}**What I want is the variance of**

*P*in the class_{O}*C*.The true values of

*P*are not known. But from each object's sample, I have

_{O}*X*, which is an estimate of

_{O}*P*. And I have

_{O}*V*, which is the variance of

_{O}*X*as an estimate of

_{O}*P*, given

_{O}*N*. (I don't know if

_{O}*X*is an unbiased estimator, but if need be, I can use a function

_{O}*f*where

*f(X*is very close to an unbiased estimator of

_{O})*f(P*.)

_{O})I think this is something I ought to know how to do. Or at least be able to find the answer via Google. But so far, no such luck. And it's not just curiosity this time, but a business need.

Note that I can't just take the variance of

*X*, because the limited sample size

_{O}*N*means that each

_{O}*X*contains variability both from the variance of

_{O}*P*(which is what I'm looking for) and from the variance of

_{O}*X*as an estimate. If I already knew the class variance of

_{O}*P*, I could use that to refine my estimate of

_{O}*P*for each object. But I'm trying to do more or less the reverse of that.

_{O}